In his fifth Asian Equation column, Michael looks at the relievers who have enjoyed modest success--and failure--making the move from Japan to America.

The last group in my analysis of the player’s who have migrated to MLB from Nippon Professional Baseball (NPB) are the relievers, the least appreciated members of a successful baseball team. Yet, of all NPB imports, they have been the most numerous (explaining the length of this article, for which I apologize in advance) and the cheapest. Diminished quality is the most obvious reason for these extremes, since starters who don’t meet MLB standards get shifted to the bullpen, and lesser talents also keep salaries down. Additionally, the typical NPB pitcher’s arsenal matches well with an MLB reliever’s skillset.

As I discussed in my last Asian Equation article, NPB is a breaking ball league, which translates better to relief than starting. A good breaking ball might fool major league hitters the first or second time they see it in a game, but it probably won’t the third or fourth time. As an illustration, here’s how batter OPS rises against two of the biggest NPB starting-pitcher busts as compared with three current MLB pitchers: the best, the most mediocre, and an old junkballer. While MLB batters’ performance improves against each pitcher the more times they see him in a game, the change is far more dramatic with Matsuzaka and Kawakami.

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Scaring up tomorrow's relief heroes on today's pile of the overlooked or undervalued.

Game Five of the 2008 World Series will long be remembered for its umpires' Beatles-inspired belief that, as John Lennon sang, "When it starts to rain, everything's the same," a philosophy which prevented sundry sodden millionaires (and Carlos Ruiz) from seeking shelter until the middle of the sixth. Despite the headlines garnered by this debacle, however, an equally intriguing story lay behind the first two relievers that Joe Maddon sent to the mound when play resumed two days later. Why does this tale of two stoppers matter? Because not long before they found themselves charged with holding the Phillies at bay in the highest of high-leverage situations, Grant Balfour and J.P. Howell were readily available. While the Rays made a point of adding this particular pair, the auction for relief help really never ends; by examining two who got away, future bidders may improve their chances of spotting tomorrow's bargains.

That Balfour and Howell were on the spot at that juncture wasn't a surprise given the duo's regular-season performance. They had been charged with similarly demanding duties (and fulfilling them capably) for some time, placing fourteenth and seventh, respectively, among major league relievers in WXRL. The farther back we go, however, the more unlikely it appears that anyone could have predicted the tandem's development into the two-headed anchor of a pennant-winning bullpen. Exactly a year before their pressure-packed outings in the World Series, the pair were coming off of disappointing 2007 campaigns followed by almost four weeks' worth of offseason. Both had posted impressive lines in Triple-A (Howell, a starter prior to this season, led the International League in strikeouts), but ERAs near eight in the majors led to the ominous appearance of labels like "journeyman" and "Quadruple-A pitcher" in their BP2K8 player comments. PECOTA wasn't especially optimistic, either; each hurler handily exceeded his 90th-percentile forecast, though it's important to note that both Howell's and Balfour's projections featured big Improve/Breakout Rates.

Finding it is fleeting, which suggests strategies for when and who to draft.

Drafting the right relievers presents an annual problem for fantasy owners. Sure, you can always take a look at their saves totals-or holds, if that's part of the game in your league-but this often ends with a few owners getting the shaft and drafting closers who have poor peripherals that drag down their other categories, just for the sake of picking up extra saves. If you overdraft for a guy guaranteed to get you saves rather than some of the poorer options that are picked up towards the back end of the draft, you may miss out on important contributors elsewhere. Today we're going to run a little exercise using WXRL, in order to see how often top relievers replicate their success, and whether it is worth it or not for you to spend (or waste) high draft picks on them.

A look at the degree to which the performance of relief pitchers is determining who might partner up for the post-season shuffle.

As the final two weeks of the season kick into gear, most of the post-season berths are still in play. Three of the six divisions-the AL East, AL Central, and NL East-feature races where the margin is two games or less, as does the race for the NL wild card. Adding to the drama is a flurry of games decided in the late innings, by timely hitting overcoming leaky bullpens. Consider Sunday's activity:

After a historically awful season, the Rays are about to turn the corner with this unit, as with several others.

The Tampa Bay Devil Rays existed for 10 seasons-the club exorcised the Devil this past November-and have been plagued for most of that decade by an inability to put a decent bullpen together. Consider for a moment that in five out of 10 years, Tampa Bay's firemen combined for a negative Adjusted Runs Prevented (ARP) total.

What exactly is ARP, and why is it used here rather than another bullpen metric, such as WXRL? ARP is a pure context-free measure of pitcher effectiveness that doesn't take into account the leverage of the situation; a counting stat that compares a reliever's performance to how an average (not replacement-level) relief pitcher would have performed in the same situations. In other words, if you are looking simply for how many more runs a bullpen prevented or allowed than average, regardless of the timing of the relief work or how it impacted the game, then ARP is your stat. It boils away luck and any statistical advantage (or disadvantage) attained from pitching well (or poorly) in more important situations to get at the bare-bones underlying performance, which is what we want to evaluate in looking at past bullpen work. As Keith Woolner explained in a 2005 mailbag:

\nMathematically, leverage is based on the win expectancy work done by Keith Woolner in BP 2005, and is defined as the change in the probability of winning the game from scoring (or allowing) one additional run in the current game situation divided by the change in probability from scoring\n(or allowing) one run at the start of the game.';
xxxpxxxxx1160988517_18 = 'Adjusted Pitcher Wins. Thorn and Palmers method for calculating a starters value in wins. Included for comparison with SNVA. APW values here calculated using runs instead of earned runs.';
xxxpxxxxx1160988517_19 = 'Support Neutral Lineup-adjusted Value Added (SNVA adjusted for the MLVr of batters faced) per game pitched.';
xxxpxxxxx1160988517_20 = 'The number of double play opportunities (defined as less than two outs with runner(s) on first, first and second, or first second and third).';
xxxpxxxxx1160988517_21 = 'The percentage of double play opportunities turned into actual double plays by a pitcher or hitter.';
xxxpxxxxx1160988517_22 = 'Winning percentage. For teams, Win% is determined by dividing wins by games played. For pitchers, Win% is determined by dividing wins by total decisions. ';
xxxpxxxxx1160988517_23 = 'Expected winning percentage for the pitcher, based on how often\na pitcher with the same innings pitched and runs allowed in each individual\ngame earned a win or loss historically in the modern era (1972-present).';
xxxpxxxxx1160988517_24 = 'Attrition Rate is the percent chance that a hitters plate appearances or a pitchers opposing batters faced will decrease by at least 50% relative to his Baseline playing time forecast. Although it is generally a good indicator of the risk of injury, Attrition Rate will also capture seasons in which his playing time decreases due to poor performance or managerial decisions. ';
xxxpxxxxx1160988517_25 = 'Batting average (hitters) or batting average allowed (pitchers).';
xxxpxxxxx1160988517_26 = 'Average number of pitches per start.';
xxxpxxxxx1160988517_27 = 'Average Pitcher Abuse Points per game started.';
xxxpxxxxx1160988517_28 = 'Singles or singles allowed.';
xxxpxxxxx1160988517_29 = 'Batting average; hits divided by at-bats.';
xxxpxxxxx1160988517_30 = 'Percentage of pitches thrown for balls.';
xxxpxxxxx1160988517_31 = 'The Baseline forecast, although it does not appear here, is a crucial intermediate step in creating a players forecast. The Baseline developed based on the players previous three seasons of performance. Both major league and (translated) minor league performances are considered.

Our servers, like the Cardinals bullpen and the A's, crashed. Only two of those get to come back.

\nMathematically, leverage is based on the win expectancy work done by Keith Woolner in BP 2005, and is defined as the change in the probability of winning the game from scoring (or allowing) one additional run in the current game situation divided by the change in probability from scoring\n(or allowing) one run at the start of the game.';
xxxpxxxxx1161098296_18 = 'Adjusted Pitcher Wins. Thorn and Palmers method for calculating a starters value in wins. Included for comparison with SNVA. APW values here calculated using runs instead of earned runs.';
xxxpxxxxx1161098296_19 = 'Support Neutral Lineup-adjusted Value Added (SNVA adjusted for the MLVr of batters faced) per game pitched.';
xxxpxxxxx1161098296_20 = 'The number of double play opportunities (defined as less than two outs with runner(s) on first, first and second, or first second and third).';
xxxpxxxxx1161098296_21 = 'The percentage of double play opportunities turned into actual double plays by a pitcher or hitter.';
xxxpxxxxx1161098296_22 = 'Winning percentage. For teams, Win% is determined by dividing wins by games played. For pitchers, Win% is determined by dividing wins by total decisions. ';
xxxpxxxxx1161098296_23 = 'Expected winning percentage for the pitcher, based on how often\na pitcher with the same innings pitched and runs allowed in each individual\ngame earned a win or loss historically in the modern era (1972-present).';
xxxpxxxxx1161098296_24 = 'Attrition Rate is the percent chance that a hitters plate appearances or a pitchers opposing batters faced will decrease by at least 50% relative to his Baseline playing time forecast. Although it is generally a good indicator of the risk of injury, Attrition Rate will also capture seasons in which his playing time decreases due to poor performance or managerial decisions. ';
xxxpxxxxx1161098296_25 = 'Batting average (hitters) or batting average allowed (pitchers).';
xxxpxxxxx1161098296_26 = 'Average number of pitches per start.';
xxxpxxxxx1161098296_27 = 'Average Pitcher Abuse Points per game started.';
xxxpxxxxx1161098296_28 = 'Singles or singles allowed.';
xxxpxxxxx1161098296_29 = 'Batting average; hits divided by at-bats.';
xxxpxxxxx1161098296_30 = 'Percentage of pitches thrown for balls.';
xxxpxxxxx1161098296_31 = 'The Baseline forecast, although it does not appear here, is a crucial intermediate step in creating a players forecast. The Baseline developed based on the players previous three seasons of performance. Both major league and (translated) minor league performances are considered.

Even Alexis Gomez came from somewhere (Kansas City). Kevin tells us how the Tigers and A's acquired the rest of their postseason difference-makers.

\nMathematically, leverage is based on the win expectancy work done by Keith Woolner in BP 2005, and is defined as the change in the probability of winning the game from scoring (or allowing) one additional run in the current game situation divided by the change in probability from scoring\n(or allowing) one run at the start of the game.';
xxxpxxxxx1160846402_18 = 'Adjusted Pitcher Wins. Thorn and Palmers method for calculating a starters value in wins. Included for comparison with SNVA. APW values here calculated using runs instead of earned runs.';
xxxpxxxxx1160846402_19 = 'Support Neutral Lineup-adjusted Value Added (SNVA adjusted for the MLVr of batters faced) per game pitched.';
xxxpxxxxx1160846402_20 = 'The number of double play opportunities (defined as less than two outs with runner(s) on first, first and second, or first second and third).';
xxxpxxxxx1160846402_21 = 'The percentage of double play opportunities turned into actual double plays by a pitcher or hitter.';
xxxpxxxxx1160846402_22 = 'Winning percentage. For teams, Win% is determined by dividing wins by games played. For pitchers, Win% is determined by dividing wins by total decisions. ';
xxxpxxxxx1160846402_23 = 'Expected winning percentage for the pitcher, based on how often\na pitcher with the same innings pitched and runs allowed in each individual\ngame earned a win or loss historically in the modern era (1972-present).';
xxxpxxxxx1160846402_24 = 'Attrition Rate is the percent chance that a hitters plate appearances or a pitchers opposing batters faced will decrease by at least 50% relative to his Baseline playing time forecast. Although it is generally a good indicator of the risk of injury, Attrition Rate will also capture seasons in which his playing time decreases due to poor performance or managerial decisions. ';
xxxpxxxxx1160846402_25 = 'Batting average (hitters) or batting average allowed (pitchers).';
xxxpxxxxx1160846402_26 = 'Average number of pitches per start.';
xxxpxxxxx1160846402_27 = 'Average Pitcher Abuse Points per game started.';
xxxpxxxxx1160846402_28 = 'Singles or singles allowed.';
xxxpxxxxx1160846402_29 = 'Batting average; hits divided by at-bats.';
xxxpxxxxx1160846402_30 = 'Percentage of pitches thrown for balls.';
xxxpxxxxx1160846402_31 = 'The Baseline forecast, although it does not appear here, is a crucial intermediate step in creating a players forecast. The Baseline developed based on the players previous three seasons of performance. Both major league and (translated) minor league performances are considered.

\nMathematically, leverage is based on the win expectancy work done by Keith Woolner in BP 2005, and is defined as the change in the probability of winning the game from scoring (or allowing) one additional run in the current game situation divided by the change in probability from scoring\n(or allowing) one run at the start of the game.';
xxxpxxxxx1160835748_18 = 'Adjusted Pitcher Wins. Thorn and Palmers method for calculating a starters value in wins. Included for comparison with SNVA. APW values here calculated using runs instead of earned runs.';
xxxpxxxxx1160835748_19 = 'Support Neutral Lineup-adjusted Value Added (SNVA adjusted for the MLVr of batters faced) per game pitched.';
xxxpxxxxx1160835748_20 = 'The number of double play opportunities (defined as less than two outs with runner(s) on first, first and second, or first second and third).';
xxxpxxxxx1160835748_21 = 'The percentage of double play opportunities turned into actual double plays by a pitcher or hitter.';
xxxpxxxxx1160835748_22 = 'Winning percentage. For teams, Win% is determined by dividing wins by games played. For pitchers, Win% is determined by dividing wins by total decisions. ';
xxxpxxxxx1160835748_23 = 'Expected winning percentage for the pitcher, based on how often\na pitcher with the same innings pitched and runs allowed in each individual\ngame earned a win or loss historically in the modern era (1972-present).';
xxxpxxxxx1160835748_24 = 'Attrition Rate is the percent chance that a hitters plate appearances or a pitchers opposing batters faced will decrease by at least 50% relative to his Baseline playing time forecast. Although it is generally a good indicator of the risk of injury, Attrition Rate will also capture seasons in which his playing time decreases due to poor performance or managerial decisions. ';
xxxpxxxxx1160835748_25 = 'Batting average (hitters) or batting average allowed (pitchers).';
xxxpxxxxx1160835748_26 = 'Average number of pitches per start.';
xxxpxxxxx1160835748_27 = 'Average Pitcher Abuse Points per game started.';
xxxpxxxxx1160835748_28 = 'Singles or singles allowed.';
xxxpxxxxx1160835748_29 = 'Batting average; hits divided by at-bats.';
xxxpxxxxx1160835748_30 = 'Percentage of pitches thrown for balls.';
xxxpxxxxx1160835748_31 = 'The Baseline forecast, although it does not appear here, is a crucial intermediate step in creating a players forecast. The Baseline developed based on the players previous three seasons of performance. Both major league and (translated) minor league performances are considered.

Jim digs back and looks at the best starting efforts by the Mets and Cardinals in the era of divisional play.

\nMathematically, leverage is based on the win expectancy work done by Keith Woolner in BP 2005, and is defined as the change in the probability of winning the game from scoring (or allowing) one additional run in the current game situation divided by the change in probability from scoring\n(or allowing) one run at the start of the game.';
xxxpxxxxx1160845280_18 = 'Adjusted Pitcher Wins. Thorn and Palmers method for calculating a starters value in wins. Included for comparison with SNVA. APW values here calculated using runs instead of earned runs.';
xxxpxxxxx1160845280_19 = 'Support Neutral Lineup-adjusted Value Added (SNVA adjusted for the MLVr of batters faced) per game pitched.';
xxxpxxxxx1160845280_20 = 'The number of double play opportunities (defined as less than two outs with runner(s) on first, first and second, or first second and third).';
xxxpxxxxx1160845280_21 = 'The percentage of double play opportunities turned into actual double plays by a pitcher or hitter.';
xxxpxxxxx1160845280_22 = 'Winning percentage. For teams, Win% is determined by dividing wins by games played. For pitchers, Win% is determined by dividing wins by total decisions. ';
xxxpxxxxx1160845280_23 = 'Expected winning percentage for the pitcher, based on how often\na pitcher with the same innings pitched and runs allowed in each individual\ngame earned a win or loss historically in the modern era (1972-present).';
xxxpxxxxx1160845280_24 = 'Attrition Rate is the percent chance that a hitters plate appearances or a pitchers opposing batters faced will decrease by at least 50% relative to his Baseline playing time forecast. Although it is generally a good indicator of the risk of injury, Attrition Rate will also capture seasons in which his playing time decreases due to poor performance or managerial decisions. ';
xxxpxxxxx1160845280_25 = 'Batting average (hitters) or batting average allowed (pitchers).';
xxxpxxxxx1160845280_26 = 'Average number of pitches per start.';
xxxpxxxxx1160845280_27 = 'Average Pitcher Abuse Points per game started.';
xxxpxxxxx1160845280_28 = 'Singles or singles allowed.';
xxxpxxxxx1160845280_29 = 'Batting average; hits divided by at-bats.';
xxxpxxxxx1160845280_30 = 'Percentage of pitches thrown for balls.';
xxxpxxxxx1160845280_31 = 'The Baseline forecast, although it does not appear here, is a crucial intermediate step in creating a players forecast. The Baseline developed based on the players previous three seasons of performance. Both major league and (translated) minor league performances are considered.

The Mets and Cardinals finally got underway in a game that no player on either team had the biggest effect on.

\nMathematically, leverage is based on the win expectancy work done by Keith Woolner in BP 2005, and is defined as the change in the probability of winning the game from scoring (or allowing) one additional run in the current game situation divided by the change in probability from scoring\n(or allowing) one run at the start of the game.';
xxxpxxxxx1160760884_18 = 'Adjusted Pitcher Wins. Thorn and Palmers method for calculating a starters value in wins. Included for comparison with SNVA. APW values here calculated using runs instead of earned runs.';
xxxpxxxxx1160760884_19 = 'Support Neutral Lineup-adjusted Value Added (SNVA adjusted for the MLVr of batters faced) per game pitched.';
xxxpxxxxx1160760884_20 = 'The number of double play opportunities (defined as less than two outs with runner(s) on first, first and second, or first second and third).';
xxxpxxxxx1160760884_21 = 'The percentage of double play opportunities turned into actual double plays by a pitcher or hitter.';
xxxpxxxxx1160760884_22 = 'Winning percentage. For teams, Win% is determined by dividing wins by games played. For pitchers, Win% is determined by dividing wins by total decisions. ';
xxxpxxxxx1160760884_23 = 'Expected winning percentage for the pitcher, based on how often\na pitcher with the same innings pitched and runs allowed in each individual\ngame earned a win or loss historically in the modern era (1972-present).';
xxxpxxxxx1160760884_24 = 'Attrition Rate is the percent chance that a hitters plate appearances or a pitchers opposing batters faced will decrease by at least 50% relative to his Baseline playing time forecast. Although it is generally a good indicator of the risk of injury, Attrition Rate will also capture seasons in which his playing time decreases due to poor performance or managerial decisions. ';
xxxpxxxxx1160760884_25 = 'Batting average (hitters) or batting average allowed (pitchers).';
xxxpxxxxx1160760884_26 = 'Average number of pitches per start.';
xxxpxxxxx1160760884_27 = 'Average Pitcher Abuse Points per game started.';
xxxpxxxxx1160760884_28 = 'Singles or singles allowed.';
xxxpxxxxx1160760884_29 = 'Batting average; hits divided by at-bats.';
xxxpxxxxx1160760884_30 = 'Percentage of pitches thrown for balls.';
xxxpxxxxx1160760884_31 = 'The Baseline forecast, although it does not appear here, is a crucial intermediate step in creating a players forecast. The Baseline developed based on the players previous three seasons of performance. Both major league and (translated) minor league performances are considered.